Symbols

Say: plus Foundation

Add the two numbers on either side.

Example: 3 + 4 = 7 is read "three plus four equals seven".

Used in: every sum

Say: minus Foundation

Take the number on the right away from the number on the left. In front of a single number it means negative.

Example: 9 − 4 = 5, and −3 is "negative three".

Used in: subtraction and negative numbers

In the glossary: integer

Say: times Foundation

Multiply the two numbers. In algebra it is often left out: 3x means 3 × x.

Example: 6 × 7 = 42 is read "six times seven equals forty-two".

Used in: every product

Say: divided by Foundation

Share the left number into as many equal parts as the right number says. A fraction bar means the same.

Example: 12 ÷ 3 = 4, the same as 12/3 = 4.

Used in: division

Say: equals Foundation

Both sides have exactly the same value.

Example: 2 + 2 = 4

Used in: every equation

In the glossary: equation

Say: is not equal to Foundation

The two sides have different values.

Example: 5 ≠ 6, and π ≠ 22/7.

Used in: comparing values

Say: is less than Foundation

The left number is smaller. The open side faces the bigger number.

Example: 3 < 8

Used in: comparing numbers, inequalities

In the glossary: number line

Say: is greater than Foundation

The left number is bigger. The open side faces the bigger number.

Example: 10 > 2

Used in: comparing numbers, inequalities

In the glossary: number line

Say: is less than or equal to Foundation

The left number is smaller than, or the same as, the right number.

Example: x ≤ 5 means x can be 5 or anything below 5.

Used in: inequalities, probability (0 ≤ P(E) ≤ 1)

Say: is greater than or equal to Foundation

The left number is bigger than, or the same as, the right number.

Example: age ≥ 18 means 18 or older.

Used in: inequalities

Say: is not greater than Foundation

The left number is not bigger than the right one, so it is smaller or equal. Many Indian books use it.

Example: x ≯ 5 means the same as x ≤ 5.

Used in: inequalities

Say: is not less than Foundation

The left number is not smaller than the right one, so it is bigger or equal.

Example: Marks ≮ 33 means 33 or more.

Used in: inequalities

Say: is much less than Class 11

The left amount is smaller by a very large factor, so small beside the right one that it can often be ignored.

Example: The mass of a raindrop ≪ the mass of a cloud.

Used in: science and estimation

Say: is much greater than Class 11

The left amount is bigger by a very large factor.

Example: The distance to the Sun ≫ the width of the Earth.

Used in: science and estimation

Say: the square root of Foundation

The number that, multiplied by itself, gives the number under the sign.

Example: √49 = 7, because 7 × 7 = 49.

Used in: squares, Pythagoras, Heron's formula

In the glossary: irrational number

Say: the cube root of Foundation

The number that, multiplied by itself three times, gives the number under the sign.

Example: ³√27 = 3, because 3 × 3 × 3 = 27.

Used in: cubes and volumes

In the glossary: perfect cube (expression)

Say: x squared Foundation

x multiplied by itself. The small raised 2 is a power.

Example: 5² = 5 × 5 = 25

Used in: areas, identities

In the glossary: perfect square (expression)

Say: x cubed Foundation

x multiplied by itself three times.

Example: 4³ = 4 × 4 × 4 = 64

Used in: volumes, identities

In the glossary: perfect cube (expression)

Say: x to the power n Foundation

x multiplied by itself n times. x is the base and n is the exponent (also called the index or power).

Example: 2⁵ = 2 × 2 × 2 × 2 × 2 = 32

Used in: powers, standard form, GPs

In the glossary: geometric progression (GP)

Say: times ten to the power n Foundation

Writes a very big or very small number as a number from 1 to 10 times a power of 10.

Example: The speed of light is about 3 × 10⁸ m/s, that is 300,000,000 m/s.

Used in: science, very large and very small numbers

Say: percent Foundation

Out of every hundred. 8% means 8 out of 100, or 8/100.

Example: 8% of 500 = 8/100 × 500 = 40

Used in: percentages, probability as a percentage

Say: pie Foundation

The distance round any circle divided by its width, always about 3.14159. Written 22/7 or 3.14 in school sums.

Example: The distance round a circle of radius 7 cm is 2 × π × 7 ≈ 44 cm.

Used in: circles, arcs, sectors

In the glossary: pi (π), circumference

Say: is about Foundation

The two sides are nearly equal; the answer has been rounded.

Example: π ≈ 3.14

Used in: rounding, estimates, values of π and roots

In the glossary: approximation

Say: plus or minus Class 10

Both: one value with + and one with −, so it gives two answers at once.

Example: x² = 9 gives x = ±3, that is, 3 or −3.

Used in: square roots, the quadratic formula

Say: brackets Foundation

Work out what is inside first. They also keep together terms that belong together.

Example: 2 × (3 + 4) = 2 × 7 = 14, but 2 × 3 + 4 = 10.

Used in: order of operations, expanding

In the glossary: expansion (of an expression)

Say: square brackets Foundation

Outer brackets, used around round brackets so that you can see which pair closes which.

Example: 2[3 + (4 − 1)] = 2 × 6 = 12.

Used in: order of operations

Say: point Foundation

Separates the whole-number part from the part smaller than 1.

Example: 3.75 is read "three point seven five": 3 wholes and 75 hundredths.

Used in: decimals

In the glossary: terminating decimal

Say: point three recurring Class 9

A bar over digits means they repeat for ever.

Example: 0.3̅ = 0.333... = 1/3, and 0.1̅4̅ = 0.141414...

Used in: repeating decimals

In the glossary: repeating decimal

Say: over Foundation

The number above (or before) it is divided by the number below (or after) it.

Example: 3/4 is "three over four": three quarters.

Used in: fractions, rates

Say: times Class 9

A raised dot also means multiply; it avoids confusing × with the letter x.

Example: 3 · 4 = 12, and 2 · a · b = 2ab.

Used in: algebra

Say: is to Foundation

Compares two amounts by division.

Example: Boys : girls = 3 : 2 means 3 boys for every 2 girls.

Used in: ratio and proportion

Say: as Foundation

Says two ratios are equal.

Example: 2 : 3 :: 4 : 6 is read "2 is to 3 as 4 is to 6".

Used in: proportion

Say: and so on Foundation

The pattern carries on in the same way.

Example: 1, 3, 5, 7, … are the odd numbers.

Used in: sequences, long sums

In the glossary: sequence

Say: rupees Foundation

The Indian rupee, the money of India.

Example: ₹250 is two hundred and fifty rupees.

Used in: money problems, fares, salaries

Say: ex Class 9

A letter standing for a number we do not know yet, or one that can change.

Example: In 2x + 3 = 11, x stands for 4.

Used in: equations, polynomials, graphs

In the glossary: variable

Say: p of x Class 9

A polynomial written in the letter x; p(2) is its value when x = 2.

Example: If p(x) = x² − 3x + 2, then p(1) = 0, so 1 is a zero of p(x).

Used in: polynomials

In the glossary: polynomial

Say: f of x Class 11

The value that the rule f gives for the input x.

Example: If f(x) = 2x + 1, then f(3) = 7.

Used in: functions and graphs

Say: the absolute value of x, or mod x Class 9

The distance of x from 0, which is never negative.

Example: |−7| = 7 and |7| = 7.

Used in: distances, number line

In the glossary: absolute value

Say: is identically equal to Class 9

The two sides are equal for every value of the letters, not just some.

Example: (a + b)² ≡ a² + 2ab + b²

Used in: algebraic identities

In the glossary: algebraic identity

Say: is proportional to Foundation

One quantity is a fixed multiple of the other: double one and you double the other.

Example: Cost ∝ number of pens: 3 pens cost 3 times as much as 1.

Used in: proportion, science laws

Say: x to the minus one Class 9

A negative power means one divided by the positive power (the reciprocal).

Example: 2⁻³ = 1/2³ = 1/8.

Used in: powers, standard form

Say: the nth root of x Class 9

The number whose nth power is x; the same as x to the power 1/n.

Example: ⁴√81 = 3, because 3⁴ = 81.

Used in: powers and roots

Say: a sub n Class 9

The nth term of a sequence; the small n gives the position.

Example: For the odd numbers, a₄ = 7.

Used in: sequences, APs and GPs

In the glossary: subscript (tₙ notation), nth term

Say: the sum of Class 10

Add up the expression for every value of the counter written below and above the sign.

Example: Σₖ₌₁⁴ k = 1 + 2 + 3 + 4 = 10.

Used in: statistics (Σfx), series

In the glossary: infinite series

Say: the product of Class 11

Multiply the expression for every value of the counter.

Example: Πₖ₌₁⁴ k = 1 × 2 × 3 × 4 = 24.

Used in: products, factorials

Say: log Class 11

The power the base must be raised to, to give the number.

Example: log₂ 8 = 3, because 2³ = 8; log₁₀ 1000 = 3.

Used in: powers, growth, pH and decibels

Say: L N, or natural log Class 12

The logarithm to base e.

Example: ln e = 1 and ln 1 = 0.

Used in: calculus, growth and decay

Say: ee Class 11

A constant about 2.71828, the base of natural growth and of natural logarithms.

Example: Money growing all the time at 100% a year for one year multiplies by e ≈ 2.718.

Used in: growth, calculus

Say: eye Class 11

A number whose square is −1; it is not on the number line.

Example: i² = −1, so √(−9) = 3i.

Used in: complex numbers

In the glossary: imaginary number

Say: the floor of x Class 11

The greatest integer that is less than or equal to x.

Example: ⌊3.7⌋ = 3 and ⌊−3.7⌋ = −4.

Used in: rounding down, counting

Say: the ceiling of x Class 11

The smallest integer that is greater than or equal to x.

Example: ⌈3.2⌉ = 4: if the students fill 3.2 buses, 4 buses are needed.

Used in: rounding up, counting

Say: mod Beyond Class 12

The remainder after dividing by a number.

Example: 17 mod 5 = 2, because 17 = 3 × 5 + 2.

Used in: clock arithmetic, remainders, computing

Say: degrees Foundation

The unit of angle: a full turn is 360°.

Example: A right angle is 90°, a straight angle 180°.

Used in: angles, triangles, circles

Say: minutes Class 11

One sixtieth of a degree.

Example: 45°30′ = 45.5°.

Used in: precise angles, maps

Say: seconds Class 11

One sixtieth of a minute.

Example: 1° = 60′ = 3600″.

Used in: astronomy, maps

Say: angle Foundation

The angle at the middle letter of the three.

Example: ∠ABC is the angle at B, between BA and BC.

Used in: every geometry chapter

Say: right angle Foundation

An angle of exactly 90°. In figures it is drawn as a small square in the corner.

Example: In a right triangle, the ∟ is opposite the hypotenuse.

Used in: right triangles, perpendicular lines

In the glossary: right triangle, hypotenuse

Say: triangle Foundation

The triangle with these three corners.

Example: △ABC has sides AB, BC and CA.

Used in: triangles, congruence

Say: is perpendicular to Foundation

Meets at a right angle (90°).

Example: CM ⊥ AB: the line from the centre to the midpoint of a chord meets it at 90°.

Used in: chords, heights, coordinate axes

In the glossary: perpendicular bisector, height (altitude)

Say: is parallel to Foundation

Never meet, however far they go: they stay the same distance apart.

Example: In a rectangle ABCD, AB ∥ DC.

Used in: parallel lines, quadrilaterals

In the glossary: parallel lines

Say: is congruent to Class 9

Same shape and same size: one fits exactly on the other.

Example: △CAB ≅ △CDE by SSS, so their angles at C are equal.

Used in: congruence proofs, circle theorems

Say: is similar to Class 10

Same shape, perhaps a different size: equal angles and sides in the same ratio.

Example: △ABC ∼ △DEF when ∠A = ∠D, ∠B = ∠E and ∠C = ∠F.

Used in: similar triangles, scale drawings

Say: line segment A B Foundation

The straight piece of line from A to B, with both ends.

Example: A̅B̅ joins A to B; its length is written AB.

Used in: geometry, constructions

Say: A B Foundation

Written without a bar, two capital letters usually mean the length from A to B.

Example: AB = 5 cm.

Used in: lengths in figures

In the glossary: distance formula

Say: arc Class 9

Written over two letters, it names the arc of a circle between those points.

Example: ⌒AB (said "arc A B") is the curved part of the circle from A to B.

Used in: circles, arc length

In the glossary: arc (major and minor), arc length

Say: circle Class 9

The circle with this centre.

Example: ⊙O is the circle with centre O.

Used in: circles

In the glossary: circle, centre (of a circle)

Say: ar Foundation

The usual letter for the radius of a circle.

Example: C = 2πr and A = πr².

Used in: circles, spheres, cylinders

In the glossary: radius (plural radii)

Say: dee Foundation

The usual letter for the diameter of a circle; d = 2r.

Example: C = πd: a wheel of diameter 56 cm goes 176 cm in one turn.

Used in: circles, wheels

In the glossary: diameter

Say: radians Class 11

An angle unit: 1 radian is the angle at the centre whose arc is as long as the radius; π rad = 180°.

Example: 90° = π/2 rad.

Used in: trigonometry, arc length

In the glossary: arc length

Say: the point x, y Class 9

A point in the plane: go x along, then y up, from the origin.

Example: (3, 4) is 3 to the right and 4 up; it is 5 from the origin.

Used in: coordinate geometry, graphs

In the glossary: ordered pair, coordinates

Say: oh Class 9

The point (0, 0) where the x-axis and y-axis cross.

Example: The distance of (3, 4) from O is √(3² + 4²) = 5.

Used in: coordinate geometry

In the glossary: origin, axis

Say: em Class 9

The usual letter for the slope of a line: how far it rises for every 1 across.

Example: y = 2x + 3 has slope m = 2 and y-intercept 3.

Used in: straight lines, graphs

In the glossary: slope, y-intercept

Say: the set of Class 9

The things listed (or described) inside make one set.

Example: {1, 2, 3} is the set of the first three natural numbers; a sample space is written {H, T}.

Used in: sets, sample spaces

In the glossary: sample space

Say: is an element of, or belongs to Class 11

The thing on the left is in the set on the right.

Example: 3 ∈ {1, 2, 3}

Used in: sets, number systems

Say: is not an element of Class 11

The thing on the left is not in the set.

Example: 4 ∉ {1, 2, 3}, and √2 ∉ ℚ.

Used in: sets, number systems

In the glossary: irrational number

Say: is a proper subset of Class 11

Every element of the left set is in the right set, and the right set has at least one more.

Example: {1, 2} ⊂ {1, 2, 3}

Used in: sets

Say: is a subset of Class 11

Every element of the left set is in the right set (they may be equal).

Example: Every set A has A ⊆ A.

Used in: sets, events

In the glossary: event (probability)

Say: is not a subset of Class 11

At least one element of the left set is missing from the right set.

Example: {1, 4} ⊄ {1, 2, 3}

Used in: sets

Say: union Class 11

Everything that is in either set (or both).

Example: {1, 2} ∪ {2, 3} = {1, 2, 3}

Used in: sets, probability of A or B

Say: intersection Class 11

Only what is in both sets.

Example: {1, 2} ∩ {2, 3} = {2}

Used in: sets, probability of A and B

Say: the empty set, or phi Class 11

The set with nothing in it. Some Indian books write it φ.

Example: {even numbers that are odd} = ∅

Used in: sets, impossible events

Say: yoo Class 11

The set of everything being talked about in a problem.

Example: For digits, U = {0, 1, 2, …, 9}.

Used in: sets, Venn diagrams

Say: A dash, or the complement of A Class 11

Everything in the universal set that is not in A.

Example: If U = {1, …, 6} and A = {2, 4, 6}, then A′ = {1, 3, 5}.

Used in: sets, probability of not E

In the glossary: event (probability)

Say: A minus B Class 11

The elements of A that are not in B.

Example: {1, 2, 3} − {2} = {1, 3}

Used in: sets

Say: n of A Class 9

How many elements the set A has.

Example: n({a, e, i, o, u}) = 5, and for two coins n(S) = 4.

Used in: sets, sample spaces

In the glossary: sample space

Say: A cross B Class 11

The set of all ordered pairs with the first from A and the second from B.

Example: {1, 2} × {x, y} = {(1, x), (1, y), (2, x), (2, y)}

Used in: relations, coordinates, outcomes of two steps

In the glossary: ordered pair

Say: N, the natural numbers Class 9

The counting numbers 1, 2, 3, …

Example: 5 ∈ ℕ but 0 ∉ ℕ (in NCERT's books).

Used in: number systems

In the glossary: natural number

Say: W, the whole numbers Foundation

The natural numbers together with 0: 0, 1, 2, 3, …

Example: 0 ∈ W

Used in: number systems

In the glossary: zero

Say: Z, the integers Class 9

The whole numbers and their negatives: …, −2, −1, 0, 1, 2, … Z comes from the German Zahlen, numbers.

Example: −7 ∈ ℤ

Used in: number systems

In the glossary: integer

Say: Q, the rational numbers Class 9

Every number that can be written p/q with p and q integers and q not 0. Q stands for quotient.

Example: 3/4 ∈ ℚ and 0.3̅ ∈ ℚ, but π ∉ ℚ.

Used in: number systems

In the glossary: rational number

Say: R, the real numbers Class 9

All the rational and irrational numbers together: every point of the number line.

Example: √2 ∈ ℝ and π ∈ ℝ.

Used in: number systems

In the glossary: real number, number line

Say: C, the complex numbers Class 11

All numbers a + bi, with a and b real and i² = −1.

Example: 3 + 2i ∈ ℂ

Used in: complex numbers

In the glossary: imaginary number

Say: therefore Class 9

So: this follows from what came before.

Example: x + 3 = 5, ∴ x = 2.

Used in: proofs and worked solutions

In the glossary: corollary

Say: because Class 9

The reason for the next statement.

Example: ∵ AB = AC, ∴ ∠B = ∠C.

Used in: proofs

Say: implies Class 11

If the left is true, the right is true.

Example: x = 3 ⇒ x² = 9 (but x² = 9 does not imply x = 3).

Used in: proofs, reasoning

In the glossary: converse (of a statement)

Say: is implied by Class 11

If the right is true, the left is true.

Example: x² = 9 ⇐ x = 3

Used in: proofs

In the glossary: converse (of a statement)

Say: if and only if Class 11

Each side implies the other: a statement and its converse are both true.

Example: x + 3 = 5 ⇔ x = 2

Used in: definitions, theorems with true converses

In the glossary: converse (of a statement)

Say: not Class 11

The opposite statement: true when the statement is false.

Example: ¬(x > 3) means x ≤ 3.

Used in: logic, negation

Say: and Class 11

Both statements are true.

Example: (x > 1) ∧ (x < 5) means 1 < x < 5.

Used in: logic

Say: or Class 11

At least one of the statements is true.

Example: (x < 0) ∨ (x > 5) leaves out 0 to 5.

Used in: logic

Say: for all Class 11

The statement holds for every member.

Example: ∀ x ∈ ℝ, x² ≥ 0.

Used in: statements about every number

Say: there exists Class 11

At least one member makes the statement true.

Example: ∃ x ∈ ℕ with x + 3 = 5 (namely x = 2).

Used in: existence statements

Say: there does not exist Class 11

No member makes the statement true.

Example: ∄ x ∈ ℝ with x² = −1.

Used in: impossibility statements

In the glossary: imaginary number

Say: Q E D Class 9

Marks the end of a proof. QED stands for quod erat demonstrandum, Latin for which was to be shown.

Example: …so √2 cannot be written as p/q. ∎

Used in: proofs

In the glossary: proof by contradiction

Say: infinity Class 11

Without end: larger than any number you can name. It is not a number itself.

Example: The natural numbers go on to ∞: there is no largest one.

Used in: limits, infinite series

In the glossary: infinite series

Say: tends to Class 11

Gets closer and closer to.

Example: x → 2 means x comes as close to 2 as we like.

Used in: limits

Say: the limit as x tends to a of Class 11

The value an expression gets closer and closer to.

Example: lim as x → 2 of (x² − 4)/(x − 2) = 4, though at x = 2 itself the fraction is 0/0.

Used in: limits, derivatives

Say: delta x Class 11

How much x changes: the new value minus the old value.

Example: From x = 3 to x = 5, Δx = 2.

Used in: slopes, rates, physics

In the glossary: slope

Say: d y by d x Class 11

How fast y changes as x changes: the slope of the curve at a point.

Example: If y = x², then dy/dx = 2x, so at x = 3 the slope is 6.

Used in: rates of change, maxima and minima

In the glossary: slope

Say: f dash x, or f prime of x Class 11

The derivative of the function f.

Example: If f(x) = x³, then f′(x) = 3x².

Used in: calculus

Say: d two y by d x squared Class 12

The derivative of the derivative: how fast the slope changes.

Example: If y = x³, then d²y/dx² = 6x.

Used in: curves, acceleration

Say: the integral of Class 12

The reverse of differentiation; also a way to add up tiny pieces, such as the area under a curve.

Example: ∫ 2x dx = x² + C.

Used in: areas, calculus

Say: the integral from a to b Class 12

The area under the curve between x = a and x = b (counting area below the x-axis as negative).

Example: ∫₀¹ 2x dx = 1² − 0² = 1.

Used in: areas under curves

In the glossary: area

Say: plus C Class 12

Any fixed number; it is added because many functions have the same derivative.

Example: x² + 5 and x² − 1 both have derivative 2x, so ∫ 2x dx = x² + C.

Used in: integration

Say: partial Beyond Class 12

The derivative with respect to one letter while the others are held fixed.

Example: If f = x²y, then ∂f/∂x = 2xy.

Used in: functions of several variables, physics

Say: f of g, or f circle g Class 12

Apply g first, then f.

Example: If f(x) = x + 1 and g(x) = 2x, then (f ∘ g)(3) = f(6) = 7.

Used in: functions

Say: f inverse Class 12

The function that undoes f. It is not 1 divided by f.

Example: If f(x) = 2x, then f⁻¹(x) = x/2.

Used in: functions

Say: P of E, the probability of E Class 9

How likely the event E is, from 0 (impossible) to 1 (certain).

Example: P(head) = 1/2 for a fair coin.

Used in: probability

In the glossary: probability, event (probability)

Say: the probability of not E Class 10

The chance that E does not happen: P(not E) = 1 − P(E). Also written P(E′) or P(Ē).

Example: P(not 6) = 1 − 1/6 = 5/6.

Used in: probability

In the glossary: event (probability), probability

Say: ess Class 9

The usual letter for the set of all outcomes.

Example: For one die, S = {1, 2, 3, 4, 5, 6} and n(S) = 6.

Used in: probability

In the glossary: sample space, outcome

Say: the probability of A and B Class 11

The chance that both events happen; for independent events it is P(A) × P(B).

Example: Two tosses: P(head and head) = 1/2 × 1/2 = 1/4.

Used in: probability, tree diagrams

In the glossary: independent events, tree diagram

Say: the probability of A given B Class 12

The chance of A when we already know that B has happened.

Example: Rolling a die, P(6 | even) = 1/3: of 2, 4 and 6, one is a 6.

Used in: probability

Say: E of X Class 12

The long-run average of a random quantity.

Example: For a fair die, E(X) = (1 + 2 + 3 + 4 + 5 + 6)/6 = 3.5.

Used in: probability, games, insurance

In the glossary: law of large numbers

Say: x bar Class 10

The mean: the sum of the values divided by how many there are.

Example: For 2, 4 and 9, x̄ = 15/3 = 5.

Used in: statistics

Say: en Class 10

How many values there are in the data.

Example: For 2, 4 and 9, n = 3.

Used in: statistics

In the glossary: sample (statistics)

Say: f i Class 10

How many times the value xᵢ occurs.

Example: If the mark 7 has fᵢ = 4, four students scored 7.

Used in: frequency tables

In the glossary: relative frequency

Say: sigma f i x i Class 10

Multiply each value by its frequency and add; divide by Σfᵢ to get the mean.

Example: Marks 1, 2, 3 with frequencies 2, 3, 5: Σfᵢxᵢ = 2 + 6 + 15 = 23 and Σfᵢ = 10, so x̄ = 2.3.

Used in: the mean of grouped data

Say: c f Class 10

The running total of the frequencies up to this class.

Example: Frequencies 3, 5, 2 give cumulative frequencies 3, 8, 10.

Used in: median of grouped data, ogives

Say: aitch Class 10

The width of each class interval in a grouped table.

Example: In the classes 10 to 20, 20 to 30, 30 to 40, h = 10.

Used in: grouped data, step deviation

Say: ay Class 10

A value near the middle of the data, chosen to make the working for the mean shorter.

Example: With a = 25, the values 23, 25, 30 become deviations −2, 0, 5.

Used in: the assumed-mean method

Say: sigma Class 11

How spread out the values are around the mean: a typical distance from it.

Example: For 2, 4, 6, 8 (mean 5), σ = √5 ≈ 2.24.

Used in: statistics, spread

Say: sigma squared Class 11

The mean of the squared distances from the mean.

Example: For 2, 4, 6, 8, σ² = (9 + 1 + 1 + 9)/4 = 5.

Used in: statistics, spread

Say: n factorial Class 11

Multiply all the whole numbers from n down to 1.

Example: 5! = 5 × 4 × 3 × 2 × 1 = 120.

Used in: arrangements, probability

Say: zero factorial Class 11

Defined to be 1, so that the counting formulas also work when nothing is chosen.

Example: 0! = 1, so ⁵C₅ = 5!/(5! × 0!) = 1.

Used in: counting formulas

Say: n P r Class 11

The number of ways to arrange r things chosen from n, when order matters: n!/(n − r)!.

Example: ⁵P₂ = 5 × 4 = 20 ways to pick a captain and a vice-captain from 5.

Used in: arrangements

Say: n C r, or n choose r Class 11

The number of ways to choose r things from n, when order does not matter: n!/(r!(n − r)!).

Example: ⁵C₂ = 10 ways to choose 2 friends from 5.

Used in: choices, probability, the binomial theorem

Say: n choose r Class 11

Another way to write ⁿCᵣ, with n above r inside tall brackets.

Example: (⁴₂) = 6, the middle number of the row 1, 4, 6, 4, 1.

Used in: the binomial theorem, Pascal's triangle

In the glossary: binomial

Say: the matrix a i j Class 12

A table of numbers in rows and columns, handled as one object; aᵢⱼ is the entry in row i, column j.

Example: A 2 × 2 matrix with rows 1 2 and 3 4 has a₂₁ = 3.

Used in: matrices, systems of equations

Say: the determinant of A Class 12

A number worked out from a square matrix; for rows a b and c d it is ad − bc.

Example: For rows 1 2 and 3 4, |A| = 1 × 4 − 2 × 3 = −2.

Used in: matrices, areas, solving equations

Say: A transpose Class 12

The matrix with its rows turned into columns.

Example: Rows 1 2 and 3 4 become rows 1 3 and 2 4.

Used in: matrices

Say: A inverse Class 12

The matrix that undoes A: A × A⁻¹ = I. It exists only when |A| ≠ 0.

Example: Rows 2 0 and 0 4 have the inverse with rows 1/2 0 and 0 1/4.

Used in: solving equations with matrices

Say: eye Class 12

Ones on the main diagonal and zeros elsewhere; multiplying by I changes nothing.

Example: A × I = A for every square matrix A of the same size.

Used in: matrices

Say: vector a Class 12

A quantity with a size and a direction, drawn as an arrow.

Example: A walk of 3 m east and 4 m north is the vector 3î + 4ĵ.

Used in: physics, geometry in 3D

Say: the magnitude of a Class 12

The length of the vector.

Example: |3î + 4ĵ| = √(3² + 4²) = 5.

Used in: vectors, distances

In the glossary: Pythagoras theorem

Say: i hat, j hat, k hat Class 12

Vectors of length 1 along the x, y and z axes.

Example: The point (2, 3, 1) has position vector 2î + 3ĵ + k̂.

Used in: vectors, 3D coordinates

Say: vector A B Class 12

The arrow that goes from point A to point B.

Example: If A = (1, 2) and B = (4, 6), then AB⃗ = 3î + 4ĵ.

Used in: vectors, geometry

Say: a dot b Class 12

Multiply matching parts and add; the answer is a number.

Example: (1, 2) · (3, 4) = 1 × 3 + 2 × 4 = 11.

Used in: angles between vectors, work in physics

Say: a cross b Class 12

A vector at right angles to both a and b, whose length is the area of the parallelogram they make.

Example: î × ĵ = k̂

Used in: 3D geometry, torque in physics

Say: AL-fuh Class 9

Often names an angle, or the first zero of a quadratic; alpha particles in physics.

Example: In a triangle with angles α, β and γ, α + β + γ = 180°.

Used in: angles, zeroes of polynomials

Say: BEE-tuh Class 10

Names a second angle, or the second zero of a quadratic.

Example: If α and β are the zeroes of x² − 5x + 6, then α + β = 5 and αβ = 6.

Used in: angles, zeroes of polynomials

Say: GAM-uh Class 9

Names a third angle; gamma rays in physics.

Example: γ = 180° − α − β.

Used in: angles, physics

Say: DEL-tuh Class 10

Δ means change in; δ means a small change; Δ also marks the discriminant or the area of a triangle in some books.

Example: If the temperature goes from 20 °C to 26 °C, ΔT = 6 °C.

Used in: change, discriminant, calculus

Say: EP-si-lon Class 11

A very small positive number; ε₀ is a constant in physics.

Example: Within ε of 2 means between 2 − ε and 2 + ε.

Used in: limits, physics

Say: ZAY-tuh Beyond Class 12

The Riemann zeta function ζ(s).

Example: ζ(2) = 1 + 1/4 + 1/9 + … = π²/6.

Used in: series, number theory

In the glossary: infinite series

Say: AY-tuh Class 11

Efficiency in physics and engineering.

Example: A machine that turns 80 J of every 100 J into useful work has η = 80%.

Used in: efficiency, physics

Say: THAY-tuh Class 10

The most common letter for an unknown angle.

Example: sin θ = 1/2 when θ = 30°.

Used in: trigonometry, angles

Say: eye-OH-tuh Beyond Class 12

Rare in school maths; it is the smallest Greek letter.

Example: Because ι is so small, "not one iota" means "not the smallest bit".

Used in: rarely used

Say: KAP-uh Beyond Class 12

Curvature in geometry; a constant in some physics formulas.

Example: A circle of radius r has curvature κ = 1/r, so a smaller circle bends more.

Used in: curvature, physics

Say: LAM-duh Class 11

Wavelength in physics; an unknown multiplier in maths.

Example: Red light has a wavelength λ of about 700 nanometres.

Used in: waves, physics

Say: myoo Class 11

The prefix micro (one millionth); the mean of a whole population; the coefficient of friction.

Example: 1 μm = 0.000001 m, one micrometre.

Used in: units, statistics, friction

Say: nyoo Class 11

Frequency in physics.

Example: In c = νλ, ν is the frequency of the light and λ its wavelength.

Used in: waves, physics

Say: ksy Beyond Class 12

A variable in advanced maths.

Example: ξ often names a point somewhere in between, in theorems of calculus.

Used in: advanced maths

Say: OH-mi-kron Beyond Class 12

Looks just like the letter o, so it is almost never used in maths.

Example: Omicron was the name given to a variant of the COVID-19 virus in 2021.

Used in: rarely used

Say: pie Foundation

π is the circle constant 3.14159…; the capital Π means the product of.

Example: The area of a circle is πr².

Used in: circles, products

In the glossary: pi (π)

Say: roh Class 11

Density in physics; resistivity.

Example: Water has density ρ ≈ 1000 kg/m³.

Used in: density, physics

Say: SIG-muh Class 10

Σ means the sum of; σ is the standard deviation.

Example: Σ k² for k = 1 to 3 is 1 + 4 + 9 = 14.

Used in: sums, statistics

Say: taw Class 11

Torque in physics; some mathematicians write τ for 2π, one full turn.

Example: τ = 2π ≈ 6.283 radians is one full turn.

Used in: torque, angles

Say: UP-si-lon Beyond Class 12

Rare in school maths.

Example: Upsilon is the Greek letter from which the Latin Y was made.

Used in: rarely used

Say: fy Class 11

The golden ratio φ ≈ 1.618; also an angle; some Indian books write the empty set as φ.

Example: φ = (1 + √5)/2 ≈ 1.618, and φ² = φ + 1.

Used in: the golden ratio, angles, sets

Say: ky Beyond Class 12

The chi-squared test (χ²) in statistics.

Example: χ² measures how far observed counts are from the expected ones.

Used in: statistics

Say: sy Class 11

The wave function of an electron in chemistry and physics.

Example: In Class 11 chemistry, ψ describes where an electron in an atom is likely to be.

Used in: atomic structure

Say: oh-MAY-guh Class 10

Ω is the ohm, the unit of electrical resistance; ω is angular speed.

Example: A 10 Ω resistor carrying 2 A has 20 V across it, since V = IR.

Used in: electricity, rotation

Say: one Foundation

Stands for 1.

Example: III = 1 + 1 + 1 = 3; quadrant I is the top right quarter of the plane.

Used in: clocks, book chapters, quadrants, years

In the glossary: quadrant

Say: five Foundation

Stands for 5.

Example: VII = 5 + 1 + 1 = 7.

Used in: clocks, book chapters, years

Say: ten Foundation

Stands for 10.

Example: XXV = 10 + 10 + 5 = 25.

Used in: clocks, book chapters, years

Say: fifty Foundation

Stands for 50.

Example: LX = 50 + 10 = 60.

Used in: clocks, book chapters, years

Say: one hundred Foundation

Stands for 100.

Example: CCL = 100 + 100 + 50 = 250.

Used in: clocks, book chapters, years

Say: five hundred Foundation

Stands for 500.

Example: DC = 500 + 100 = 600.

Used in: clocks, book chapters, years

Say: one thousand Foundation

Stands for 1000.

Example: MM = 2000.

Used in: clocks, book chapters, years

Say: four Foundation

4: I before V is taken away, 5 − 1.

Example: Quadrant IV is the bottom right quarter of the plane.

Used in: clocks, book chapters, quadrants, years

In the glossary: quadrant

Say: nine Foundation

9: I before X is taken away, 10 − 1.

Example: XIX = 10 + 9 = 19.

Used in: clocks, book chapters, years

Say: forty Foundation

40: X before L is taken away, 50 − 10.

Example: XLII = 42.

Used in: clocks, book chapters, years

Say: ninety Foundation

90: X before C is taken away, 100 − 10.

Example: XCIX = 90 + 9 = 99.

Used in: clocks, book chapters, years

Say: four hundred Foundation

400: C before D is taken away, 500 − 100.

Example: CDL = 450.

Used in: clocks, book chapters, years

Say: nine hundred Foundation

900: C before M is taken away, 1000 − 100.

Example: MCMXLVII = 1000 + 900 + 40 + 7 = 1947.

Used in: clocks, book chapters, years

Say: two thousand and twenty-six Foundation

A year written in Roman numerals.

Example: MMXXVI = 1000 + 1000 + 10 + 10 + 5 + 1 = 2026.

Used in: clocks, book chapters, years